Students across the United States have made some gains but continue to lag behind many of their Asian counterparts in reading, math and science, according to the results of two international tests released Tuesday.

U.S. fourth-graders’ math and reading scores improved since the last time students took the tests several years ago, while eighth-graders remained stable in math and science. Americans outperformed the international average in all three subjects but remained far behind students in such places as Singapore and Hong Kong, especially in math and science.

Jack Buckley, commissioner of the National Center for Education Statistics, said the results leave him “optimistic” about the United States’ performance, particularly given that many higher-performing nations do not deal with the same wide range of student and family income, backgrounds and language ability.

“We have a large and diverse population of kids to educate, and I think these results show that we’re doing pretty well,” Buckley told reporters Monday.

Still, the results are likely to fuel concerns among U.S. business leaders, policymakers and many educators, who worry that the country will not be able to compete globally if U.S. students cannot keep up academically with their peers around the world.

In fourth-grade math, for example, students in Singapore, Korea, Hong Kong, Taiwan, Japan, Northern Ireland and the Flemish region of Belgium outperformed U.S. students. Finland, England and Russia also posted higher average scores, but the differences were statistically insignificant.

The results were drawn from the 2011 Progress in International Reading Literacy Study, known as PIRLS, and the Trends in International Mathematics and Science Study, referred to as TIMSS.

The literacy test, which fourth-graders take every five years, was administered to a representative sample of public- and private-school students in 53 countries, states and regions. The math test is taken every four years by fourth- and eighth-graders in more than 55 countries, states and regions.

A handful of U.S. states volunteered to give the tests to their students and be graded as if they were countries, to see how their students perform compared with international benchmarks. Virginia, Maryland and the District were not among those states.

Florida, the only state that volunteered to take the reading exam, emerged as a leading scorer on that test among all countries and states that administered it. Only students in Hong Kong scored higher, but the difference was not significant.

Buckley said the results demonstrate that Florida is “capable of performing as well as or better than some of the countries and other education systems that are regarded as international leaders.”

But skeptics say Florida’s unusually strong performance is an illusion.

Boston College professor Walter Haney said Florida’s scores are misleading because, since 2004, Florida has held back third-grade students who are not reading on grade level, preventing them from advancing to the fourth grade, when the test is administered. As a result, test-takers in Florida do not include students who are struggling with reading, Haney said.

In the 2010-2011 school year, the fourth grade in Florida had 4 percent fewer students than the third grade from the previous year, Haney said. That meant a significant number of weak readers were held back and weren’t among the fourth-graders who took the test. Students who are held back are more likely to drop out of school, Haney said.

“It’s really a tragedy in the making,” he said. “When kids are flunked, if they’re over-age by the time they hit high school, 65 to 90 percent will drop out. It’s not a sound educational strategy. It doesn’t increase achievement and dramatically increases the possibility they will drop out.”

Several states that took the test independently scored higher than the U.S. average in eighth-grade math, including North Carolina, Indiana, Massachusetts and Minnesota. North Carolina also outscored the U.S. average in fourth-grade math. Massachusetts, Minnesota and Colorado exceeded the U.S. average in eighth-grade science.

Even those high performers have much ground to gain on international leaders. In Singapore, for example, 40 percent of eighth-grade students scored high enough in science to be deemed “advanced.” In Massachusetts, about one-quarter of students reached that mark.

The U.S. results showed discrepancies among student groups, mirroring gaps that exist in many measures of academic achievement.

White, Asian and multiracial students scored higher than the U.S. average on the reading test, for example, while black and Hispanic students scored lower than the U.S. average. Meanwhile, students from schools with low poverty rates posted better average scores than students from high-poverty schools.

The international exams also showed, across countries and subjects, that students who have teachers with at least a decade of experience performed better, as did students who had teachers with high levels of career satisfaction.

Lyndsey Layton has been covering national education since 2011, writing about everything from parent trigger laws to poverty’s impact on education to the shifting politics of school reform.

Emma Brown writes about national education and about people with a stake in schools, including teachers, parents and kids.

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